Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 263
Posted:
May 14, 2013 2:46 AM


In article <d6f681f1613b4e57a3365ab501a04645@wb17g2000pbc.googlegroups.com>, Graham Cooper <grahamcooper7@gmail.com> wrote:
> On May 14, 1:36 pm, Virgil <vir...@ligriv.com> wrote: > > In article > > <d8620fe3928d4bc5bf24b16bee326...@wb17g2000pbc.googlegroups.com>, > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > On May 14, 11:09 am, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > <4f6cc18e90b2415e83aa963e1c083...@n5g2000pbg.googlegroups.com>, > > > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > such as Virgil's favorite number! > > > > > > > 0.44444454444444444445444444545544444444445444444444444... > > > > > > That denotes, as yet, any of a range of real numbers, not any specific > > > > one, and whichever ones in that range Graham finds his favorite, none of > > > > them are anything like my favorite. > > > > > Real numbers of that form are all you need to show > > > > I don't need to show any any such numbers. > > > > > > > > >  POINTS  >  INFINITE LIST  > > > > > between these 2 bars! > > > > > >< > > > > > Here's another one > > > > > 0.4444444444445444444444454444445444444444454444445444444... > > > > > Remember your hero CANTOR showed you how to CONSTRUCT that number! > > > > > You post 20 times a day the Algorithm (sic) to construct that real! > > > > The algorithm I regularly post, and Cantor first used, is for binary > > sequences not decimals. > > > > Neither type of "antidiagonal" is defined without an infinite list of > > sequences of the the appropriate type from which to build it, which > > lists you have not provided, so no antidiagonal need exist until you do. > > > > Such algorithms have been posted 100 times. > > Though You have no clue what Cantor's Missing Set function actually > does. > > > SET1 = { 1 , 3 , 6 } > SET2 = { 1 , 5 , 11 } > SET3 = { 2 , 4 , 6, 8 , 10 , ... } > SET4 = { 4 , 5, 6, 7, 8 } > > [VIRGIL] > > Given an arbitrary function f from N to the powerset of N (set of > all subsets of N), the set S = {n in N  ~ n in f(n)} is a subset of > N not in the image of f, and thus is a proper "Cantor's missing > set". > > You learnt this magic formula off by heart and you have no idea how to > apply it!
I have learnt the quadratic formula off by heart, too, though, at need I can derive it from the quadratic equation, a*x^2 + b*x + c = 0, and apply it. > > and the Missing Set from the above enumeration is.... ?
In order to be able to use the definition "S = {n in N  ~ n in f(n)}" and thus determine which sets are missing in the image of a given function, f: N > 2^N, one must first be able to determine all the values of that function, i.e., one subset of N for each member of N..
If you only give me
f(1) = { 1 , 3 , 6 } f(2) = { 1 , 5 , 11 } f(3) = { 2 , 4 , 6, 8 , 10 , ... } f(4) = { 4 , 5, 6, 7, 8 }
All I know so far is that that your f cannot be such a function because 1 is in f(1) and 4 is in f(4). 

